AP Statistics: Chapter 7 Vocabulary

Unbiased Estimator

A statistic used to estimate a parameter with a mean of its sampling distribution equal to the true value of the parameter being estimated.

Biased Estimator

A statistic used to estimate a parameter with a mean of its sampling distribution not equal to the true value of the parameter being estimated.

Statistic

A number that describes some characteristic of a sample. The value of a statistic can be computed directly from the sample. This can be used to estimate an unknown parameter.

Parameter

A number that describes some characteristic of the population. This is usually unknown because it is hard to examine an entire population.

Sampling Distribution of a Sample Mean (Normal Population)

A population that is normally distributed with mean μ and standard deviation σ with a sampling distribution of X that has a Normal Distribution with mean and standard deviation. The 10% condition must be met.

Sampling Distribution

The distribution of a statistic & its values taken by the statistic in all possible samples of the same size from the same population.

Sampling Variability

The fact that the value of a statistic varies in repeated random sampling.

Central Theorem Limit (CTL)

This states that when 'N' is large, the sampling distribution of the sample mean is approximately Normal. First, draw an SRS of size 'N' from any population with mean μ and finite standard deviation σ.

Population Distribution

This gives the values of the variable for all the individuals in the population.

Variability of a Statistic

This is described by the spread of its sampling distribution. This spread is determined primarily by the size of the random sample. Larger samples give smaller spread. The spread of the sampling distribution does not depend on the size of the population, as long as the population is at least 10 times larger than the sample.

Sampling Distribution of 'P'

This measures good the statistic is as an estimate of the parameter. Ask, "What would happen if we took many samples?" The sampling distribution of 'P' answers this question. This is approximately normal as 'N' increases under the conditions that the population is at least 10 times larger than the sample.

Normal Condition for Sample Means

This states that if the population distribution is Normal, then so is the sampling distribution of X. This is true no matter what the sample size is. Also, if the population distribution is not Normal, the central limit theorem states that the sampling distribution of X will be approximately Normal if 'N' ≥ 30.